Intermediate-series sl2 module
= Intermediate-series sl2 module
{c}
An intermediate-series $\mathfrak{sl}_2$-module has one-dimensional weight spaces indexed by all integers. In the basis $(w_i)_{i\in\mathbb Z}$, one useful normalization is
$$
hw_i=(a+2i)w_i,\qquad fw_i=w_{i-1},\qquad
ew_i=(b-ia-i(i+1))w_{i+1}.
$$
It is irreducible exactly when every raising coefficient is nonzero.